Divide :
$5 \frac{1}{2}$ $\div$ $14$

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Solution

Division of fraction by a whole number :
Here, we have given a fraction and a whole number. To divide a fraction by a natural number, we multiply the fraction by the reciprocal of the natural number.
The given fraction is $5 \frac{1}{2}$ (which is a mixed fraction) and the given natural number is $14$ .
Reciprocal of natural number $14$ is $\frac{1}{14}$ .
Firstly, converting $5 \frac{1}{2}$ into improper form. We have
$5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{11}{2}$
Now, multiplying the given fraction $\frac{11}{2}$ with the reciprocal of $14$ i.e. $\frac{1}{14}$ .
Thus, $\frac{11}{2}$ $\times$ $\frac{1}{14}$ $=$ $\frac{11 \times 1}{2 \times 14}$ [multiplying the numerators and denominators of the fractions]
$=$ $\frac{11}{28}$
Therefore, $5 \frac{1}{2}$ $\div$ $14$ $=$ $\frac{11}{28}$

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